More than 2500 years ago, the pre-Socratic Greek philosopher Heraclitus stated that the “only thing that is constant is change. Thereafter, philosophers and scientists have attempted to outline the trajectory of this change. Even though change itself is constant the rate of change is rarely constant. The ‘slow-fast-slow’ trajectory of the Sigmoid(S) curve describes a vast range of natural and historical phenomenon. Things happen slowly often imperceptibly and then thrust forward exponentially, and subsequently taper off towards the end. Phenomena such as Stephen J. Gould’s theory of punctuated equilibrium explains speciation data, Joseph’s Schumpeter’s creative destruction can be modeled via a S-curve, Thomas Kuhn’s paradigm shifts in science can be explained by S – curves. The S-curve is intimately related to the all-pervasive Gaussian distribution via the differential. The convexity of the S-curve explains the diminishing returns of the economics and the concavity incorporates the exponential returns of compounding. The universe seems to be filled with S-curves, however, the nature of the relationship makes them invisible to us. They are more surprising, the longer we have been waiting for them, and maximally surprising, right before they happen.
Learning, skill-building, personal development also follows the S – curve framework of ‘slow-fast-slow.’ In French, the verb essayer means ‘to attempt’ or ‘to embark upon.’ I hope to use the essays on this website to broaden my mental frameworks because “writing is thinking on paper” and “thinking is the endeavor to capture reality by the means of ideas.” As the historian, Will Durant so eloquently stated, “the only real revolution is in the enlightenment of the mind and the improvement of character, the only real emancipation is individual.”